The UT1 Intensive results heavily depend on the celestial pole offset (CPO) model used during data processing. Since accurate CPO values are available with a delay of two to four weeks, CPO predictions are necessarily applied to the UT1 Intensive data analysis, and errors in the predictions can influence the operational UT1 accuracy. In this paper we assess the real accuracy of CPO prediction using the actual IERS and PUL predictions made in 2007-2009. Also, results of operational processing were analyzed to investigate the actual impact of EOP prediction errors on the rapid UT1 results. It was found that the impact of CPO prediction errors is at a level of several microseconds, whereas the impact of the inaccuracy in the polar motion prediction may be about one order of magnitude larger for ultra-rapid UT1 results. The situation can be amended if the IERS Rapid solution will be updated more frequently.